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We present a JASMIN-based two-dimensional parallel implementation of an adaptive combined preconditioner for the solution of linear problems arising in the finite volume discretisation of one-group and multi-group radiation diffusion equations. We first propose the attribute of patch-correlation for cells of a two-dimensional monolayer piecewise rectangular structured grid without any suspensions based on the patch hierarchy of JASMIN, classify and reorder these cells via their attributes, and derive the conversion of cell-permutations. Using two cell-permutations, we then construct some parallel incomplete LU factorisation and substitution algorithms, to provide our parallel -GMRES solver with the help of the default BoomerAMG in the HYPRE library. Numerical results demonstrate that our proposed parallel incomplete LU preconditioner (ILU) is of higher efficiency than the counterpart in the Euclid library, and that the proposed parallel -GMRES solver is more robust and more efficient than the default BoomerAMG-GMRES solver.

The effect of A-site vacancy order-disorder states on diffuse phase transition (DPT) of tungsten bronze Pb1−xBaxNb2O6 (PBN) ferroelectrics has been investigated. The A-site vacancy disordered PBN ceramics exhibit notable variations of the Curie temperatures (i.e., the temperatures at the dielectric maximum permittivities) up to 12 °C in response to frequency changed from 0.1 KHz to 100 KHz. The largest frequency dispersion occurred at the morphotropic phase boundary of 1 − X = 0.63, along with the lowest Curie point. In contrast, the A-site vacancy ordered PBN ceramics present little frequency dispersion in the range of 2 °C from 0.1 KHz to 100 KHz. Dielectric constants of the disordered PBN ceramics were generally higher than those of the ordered ones. In comparison with the ordered PBN ceramics, the Curie points of the disordered ceramics were shifted from lower to higher temperature as the Pb2+ cation percentage was decreased; i.e., the Curie temperatures of the disordered PBN ceramics were lower than those of the ordered ones when 1 − X ≥ 0.70, but higher when 1 − X ≤ 0.65. These differences are suggested to inherently result from the A-site vacancy order-disorder states. The relationship between the A-site vacancy order-disorder states and the dielectric properties has also been confirmed with studies of thermal hysteresis.

The order-disorder states of the A-site vacancy of PBN solid solution affected by different thermal treatments were studied with the aid of High Resolution Electron Microscopy (HREM). PBN ceramics around the morphotropic phase boundary were prepared through two routes to control ordering degree of the A-site vacancy: (1) samples through quenching processes resulted in chaotic states of the A-site vacancies and misfit anti-phase boundary; (2) samples through slow cooling led to an ordered structure of the vacancies in the A1-site. The ordered A1-site vacancies were modulated by interchanges of the sublattices of the ordered vacancies and the Pb2+ cations in the A1-sites along both and orientations, forming a narrow discommensurate wall between two anti-phase domains. The anti-phase domains were observed as a regular belt structure with dimensions of about 45 nm × (≥120) nm. The belt nano-domain structures were a result of quasi-equilibrium thermodynamic processes.

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